Communication Dans Un Congrès Année : 2023

Nuancing stability for self-sustained musical instruments: transient durations and basins of attraction

Résumé

We are interested in the behavior of self-sustained musical instruments, such as wind instruments and bowed string instruments. Those dynamical systems can be modeled by autonomous equations. The quasi-static analysis of those equations is thoroughly represented in the literature. In this framework, stationary solutions are calculated, along with their local stability. However, those systems may be multistable: multiple locally stable solutions coexist for identical parameter values. Transient analysis notions are then needed to predict the actual regime obtained. This work aims at proposing analysis tools and graphical representations to complement the quasi-static analysis. On the one hand, we nuance the notion of stability using basins of attraction (determined with Support Vector Machines). On the other hand, we propose to enrich bifurcation diagrams with information about transient durations. Those methods are applied to a fifth order Van der Pol oscillator, which is an archetype of a self-sustained musical instrument model.

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hal-04800154 , version 1 (23-11-2024)

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Martin Pégeot, Christophe Vergez, Jean-Baptiste Doc, Vincent Fréour, Tom Colinot. Nuancing stability for self-sustained musical instruments: transient durations and basins of attraction. Forum Acusticum, Sep 2023, Turin, Italy. ⟨10.61782/fa.2023.0180⟩. ⟨hal-04800154⟩
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